Exploratory Data Analysis
Remark: covers Chapter 3 of the Tan book in Part
Organization
1. Why Exloratory Data Analysis?
2. Summary Statistics
3. Visualization
Tan,Steinbach, Kumar: Exploratory Data Analysis (with modifications by Ch. Eick)
1. Why Data Exploration?
A preliminary exploration of the data to
better understand its characteristics.

Key motivations of data exploration include
– Helping to select the right tool for preprocessing, data analysis and data
mining
– Making use of humans’ abilities to recognize patterns


People can recognize patterns not captured by data analysis tools
Related to the area of Exploratory Data Analysis (EDA)
– Created by statistician John Tukey
– Seminal book is Exploratory Data Analysis by Tukey
– A nice online introduction can be found in Chapter 1 of the NIST
Engineering Statistics Handbook
http://www.itl.nist.gov/div898/handbook/index.htm
Tan,Steinbach, Kumar: Exploratory Data Analysis (with modifications by Ch. Eick)
Exploratory Data Analysis
Get Data
Exploratory Data Analysis
Preprocessing
Data Mining
Tan,Steinbach, Kumar: Exploratory Data Analysis (with modifications by Ch. Eick)
Techniques Used In Data Exploration

In EDA, as originally defined by Tukey
– The focus was on visualization
– Clustering and anomaly detection were viewed as
exploratory techniques
– In data mining, clustering and anomaly detection are
major areas of interest, and not thought of as just
exploratory

In our discussion of data exploration, we focus
on
1. Summary statistics
2. Visualization
Tan,Steinbach, Kumar: Exploratory Data Analysis (with modifications by Ch. Eick)
Iris Sample Data Set

Many of the exploratory data techniques are illustrated
with the Iris Plant data set.
– Can be obtained from the UCI Machine Learning Repository
http://www.ics.uci.edu/~mlearn/MLRepository.html
– From the statistician Douglas Fisher
– Three flower types (classes):
Setosa
 Virginica
 Versicolour

– Four (non-class) attributes
Sepal width and length
 Petal width and length

Virginica. Robert H. Mohlenbrock. USDA
NRCS. 1995. Northeast wetland flora: Field
office guide to plant species. Northeast National
Technical Center, Chester, PA. Courtesy of
USDA NRCS Wetland Science Institute.
Tan,Steinbach, Kumar: Exploratory Data Analysis (with modifications by Ch. Eick)
2. Summary Statistics

Summary statistics are numbers that summarize
properties of the data
– Summarized properties include frequency, location and
spread

Examples:
location - mean
spread - standard deviation
– Most summary statistics can be calculated in a single
pass through the data
Tan,Steinbach, Kumar: Exploratory Data Analysis (with modifications by Ch. Eick)
Frequency and Mode
 The
frequency of an attribute value is the
percentage of time the value occurs in the
data set
– For example, given the attribute ‘gender’ and a
representative population of people, the gender
‘female’ occurs about 50% of the time.
The mode of a an attribute is the most frequent
attribute value
 The notions of frequency and mode are typically
used with categorical data

Tan,Steinbach, Kumar: Exploratory Data Analysis (with modifications by Ch. Eick)
R Box Plots (different from textbook)

http://chartsgraphs.wordpress.com/2008/11/18/boxplots-r-does-them-right/
R Box Plots
Corrected on: 9/9/2013
– Invented by J. Tukey
– Another way of displaying the distribution of data
– Following figure shows the basic part of a box plot
outlier
Maximum (or at most 1.5
IQR off the 75th percentile)
75th percentile
IQR
50th percentile
25th percentile
Minimum (or at most 1.5 IQR
off the 25th percentile)
Tan,Steinbach, Kumar: Exploratory Data Analysis (with modifications by Ch. Eick)
Percentiles

For continuous data, the notion of a percentile is
more useful.
Given an ordinal or continuous attribute x and a
number p between 0 and
100, the pth percentile is
x
a value x p of x such that p% of the observed
values of x are less than x p .
p
For
instance, the 50th percentile is the value x50%
such that 50% ofall values of x are less than x50%.
Tan,Steinbach, Kumar: Exploratory Data Analysis (with modifications by Ch. Eick)

Measures of Location: Mean and Median
The mean is the most common measure of the
location of a set of points.
 However, the mean is very sensitive to outliers.
 Thus, the median or a trimmed mean is also
commonly used.

Tan,Steinbach, Kumar: Exploratory Data Analysis (with modifications by Ch. Eick)
Measures of Spread: Range and Variance
Range is the difference between the max and min
0, 2, 3, 7, 8
 The variance or standard deviation

11.5
standard_deviation(x)= sx

3.3
However, this is also sensitive to outliers, so that
other measures are often used.
2.8
(Mean Absolute Deviation) [Han]
(Absolute Average Deviation) [Tan]
3
(Median Absolute Deviation)
5
Tan,Steinbach, Kumar: Exploratory Data Analysis (with modifications by Ch. Eick)
Correlation

To be discussed when we discuss scatter plots
Tan,Steinbach, Kumar: Exploratory Data Analysis (with modifications by Ch. Eick)
3. Visualization
Visualization is the conversion of data into a visual
or tabular format so that the characteristics of the
data and the relationships among data items or
attributes can be analyzed or reported.

Visualization of data is one of the most powerful
and appealing techniques for data exploration.
– Humans have a well developed ability to analyze large
amounts of information that is presented visually
– Can detect general patterns and trends
– Can detect outliers and unusual patterns
Tan,Steinbach, Kumar: Exploratory Data Analysis (with modifications by Ch. Eick)
Example: Sea Surface Temperature

The following shows the Sea Surface
Temperature (SST) for July 1982
– Tens of thousands of data points are summarized in a
single figure
Tan,Steinbach, Kumar: Exploratory Data Analysis (with modifications by Ch. Eick)
Representation
Is the mapping of information to a visual format
 Data objects, their attributes, and the relationships
among data objects are translated into graphical
elements such as points, lines, shapes, and
colors.
 Example:

– Objects are often represented as points
– Their attribute values can be represented as the
position of the points or the characteristics of the
points, e.g., color, size, and shape
– If position is used, then the relationships of points, i.e.,
whether they form groups or a point is an outlier, is
easily perceived.
Tan,Steinbach, Kumar: Exploratory Data Analysis (with modifications by Ch. Eick)
Arrangement
Is the placement of visual elements within a
display
 Can make a large difference in how easy it is to
understand the data
 Example:

Tan,Steinbach, Kumar: Exploratory Data Analysis (with modifications by Ch. Eick)
Example: Visualizing Universities
Tan,Steinbach, Kumar: Exploratory Data Analysis (with modifications by Ch. Eick)
Selection
Is the elimination or the de-emphasis of certain
objects and attributes
 Selection may involve the chosing a subset of
attributes

– Dimensionality reduction is often used to reduce the
number of dimensions to two or three
– Alternatively, pairs of attributes can be considered

Selection may also involve choosing a subset of
objects
– A region of the screen can only show so many points
– Can sample, but want to preserve points in sparse
areas
Tan,Steinbach, Kumar: Exploratory Data Analysis (with modifications by Ch. Eick)
Visualization Techniques: Histograms

Histogram
– Usually shows the distribution of values of a single variable
– Divide the values into bins and show a bar plot of the number of
objects in each bin.
– The height of each bar indicates the number of objects
– Shape of histogram depends on the number of bins

Example: Petal Width (10 and 20 bins, respectively)
Tan,Steinbach, Kumar: Exploratory Data Analysis (with modifications by Ch. Eick)
Two-Dimensional Histograms
Show the joint distribution of the values of two
attributes
 Example: petal width and petal length

– What does this tell us?
Tan,Steinbach, Kumar: Exploratory Data Analysis (with modifications by Ch. Eick)
Visualization Techniques: Histograms



Several variations of histograms exist: equi-bin(most
popular), other approaches use variable bin sizes…
Choosing proper bin-sizes and bin-starting points is a non
trivial problem!!
Example Problem from the midterm exam 2009: Assume you have an
attribute A that has the attribute values that range between 0 and 6; its
particular values are: 0.62 0.97 0.98 1.01. 1.02 1.07 2.96 2.97 2.99
3.02 3.03 3.06 4.96 4.97 4.98 5.02 5.03 5.04. Assume this attribute A
is visualized as a equi-bin histogram with 6 bins: [0,1), [1,2), [2,3],[3,4),
[4,5), [5,6]. Does the histogram provide a good approximation of the
distribution/density function of attribute A? If not, provide a better
histogram for attribute A. Give reasons for your answers! [7]
Tan,Steinbach, Kumar: Exploratory Data Analysis (with modifications by Ch. Eick)
Visualization Techniques: Box Plots

Box Plots
– Invented by J. Tukey
– Another way of displaying the distribution of data
– Following figure shows the basic part of a box plot
outlier
90th percentile
75th percentile
50th percentile
25th percentile
10th percentile
Tan,Steinbach, Kumar: Exploratory Data Analysis (with modifications by Ch. Eick)
Example of Box Plots

Box plots can be used to compare different attributes and the
same attribute for instances of different classes.
Tan,Steinbach, Kumar: Exploratory Data Analysis (with modifications by Ch. Eick)
Visualization Techniques: Scatter Plots

Scatter plots
– Attributes values determine the position
– Two-dimensional scatter plots most common, but can
have three-dimensional scatter plots
– Often additional attributes can be displayed by using
the size, shape, and color of the markers that
represent the objects
– It is useful to have arrays of scatter plots can
compactly summarize the relationships of several pairs
of attributes
For prediction scatter plots see:
http://en.wikipedia.org/wiki/Scatter_plot
http://en.wikipedia.org/wiki/Correlation (Correlation)
 See example for classification scatter plots on the next slide

Tan,Steinbach, Kumar: Exploratory Data Analysis (with modifications by Ch. Eick)
Scatter Plot Array of Iris Attributes
Tan,Steinbach, Kumar: Exploratory Data Analysis (with modifications by Ch. Eick)
Scatter Plot Old Faithful Eruptions
http://en.wikipedia.org/wiki/Old_Faithful
Tan,Steinbach, Kumar: Exploratory Data Analysis (with modifications by Ch. Eick)
Visualization Techniques: Contour Plots

Contour plots
– Useful when a continuous attribute is measured on a
spatial grid
– They partition the plane into regions of similar values
– The contour lines that form the boundaries of these
regions connect points with equal values
– The most common example is contour maps of
elevation
– Can also display temperature, rainfall, air pressure,
etc.

An example for Sea Surface Temperature (SST) is provided
on the next slide
Tan,Steinbach, Kumar: Exploratory Data Analysis (with modifications by Ch. Eick)
Contour Plot Example: SST Dec, 1998
Celsius
Tan,Steinbach, Kumar: Exploratory Data Analysis (with modifications by Ch. Eick)
Visualization Techniques: Parallel Coordinates

Parallel Coordinates
– Used to plot the attribute values of high-dimensional
data
– Instead of using perpendicular axes, use a set of
parallel axes
– The attribute values of each object are plotted as a
point on each corresponding coordinate axis and the
points are connected by a line
– Thus, each object is represented as a line
– Often, the lines representing a distinct class of objects
group together, at least for some attributes
– Ordering of attributes is important in seeing such
groupings
Tan,Steinbach, Kumar: Exploratory Data Analysis (with modifications by Ch. Eick)
Parallel Coordinates Plots for Iris Data
Tan,Steinbach, Kumar: Exploratory Data Analysis (with modifications by Ch. Eick)
Other Visualization Techniques

Star Coordinate Plots
– Similar approach to parallel coordinates, but axes radiate from a
central point
– The line connecting the values of an object is a polygon

Chernoff Faces
– Approach created by Herman Chernoff
– This approach associates each attribute with a characteristic of a
face
– The values of each attribute determine the appearance of the
corresponding facial characteristic
– Each object becomes a separate face
– Relies on human’s ability to distinguish faces
– http://people.cs.uchicago.edu/~wiseman/chernoff/
– http://kspark.kaist.ac.kr/Human%20Engineering.files/Chernoff/Ch
ernoff%20Faces.htm#
Tan,Steinbach, Kumar: Exploratory Data Analysis (with modifications by Ch. Eick)
Star Plots for Iris Data
Setosa
Versicolour
Pedal length
Sepal Width
Virginica
Sepal length
Pedal width
Tan,Steinbach, Kumar: Exploratory Data Analysis (with modifications by Ch. Eick)
Chernoff Faces for Iris Data
Translation: sepal lengthsize of face; sepal width forhead/jaw relative to arc-length;
Pedal lengthshape of forhead; pedal width shape of jaw; width of mouth…; width between eyes…
Setosa
Versicolour
Virginica
Tan,Steinbach, Kumar: Exploratory Data Analysis (with modifications by Ch. Eick)
Useful Background “Engineering St. Handbook”
– http://www.itl.nist.gov/div898/handbook/eda/section1/e
da15.htm (graphical techniques)
– http://www.itl.nist.gov/div898/handbook/eda/section3/e
da35.htm (quantitative analysis)
– http://www.itl.nist.gov/div898/handbook/eda/section2/e
da23.htm (testing assumptions)
– http://www.itl.nist.gov/div898/handbook/eda/section3/e
da34.htm (survey graphical techniques)
Remark: The material is very good if your focus is on
prediction, hypothesis testing, clustering; however,
providing good visualizations/statistics for classification
problems is not discussed much…
Tan,Steinbach, Kumar: Exploratory Data Analysis (with modifications by Ch. Eick)